Question 564891:
Solving equations: find the real number solutions of the equation.
g³ + 3g² - g - 3 = 0
any help would be appreciated, thank you, Mike
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website!
g³ + 3g² - g - 3 = 0
Factor the first two terms g³ + 3g² by taking out the common factor
g², getting g²(g + 3).
Factor the last two terms -g - 3 by taking out the common factor
-1, getting -1(g + 3).
So the equation is now:
g²(g + 3) - 1(g + 3) = 0
Now factor out the common factor (g + 3)
(g + 3)(g² - 1) = 0
Now the expression in the second parentheses g² - 1 can be factored as the
difference of two squares as (g - 1)(g + 1) and the equation is now:
(g + 3)(g - 1)(g + 1) = 0
Us the principle of zero factors and set each factor = 0, and solve:
g + 3 = 0; g - 1 = 0; g + 1 = 0
g = -3; g = 1; g = -1
The solutions are these three: -3, 1, and -1.
Edwin
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